Method and system for magnetic resonance imaging

ABSTRACT

An MRI pulse sequence is disclosed. The pulse sequence involves a plurality of slice selective pulses which each individually have a desired rotation that is less than or equal to the total desired rotation. The slice selective pulses each cause a rotation about respective axes, which may be different to each other. Optionally phase correction (re-phasing) gradients can also be included in the pulse sequence.

CLAIM OF PRIORITY

This application is a continuation of U.S. patent application Ser. No.15/548,734 filed on Aug. 3, 2017, which is the U.S. National Phase under35 U.S.C. § 371 of Int'l Appl. No. PCT/AU2016/050068 filed on Feb. 5,2016, designating the United States and published in English on Aug. 11,2016 as WO2016/123674A1, which claims priority to Australia Pat. Appl.No. 2015900378 filed on Feb. 6, 2015 and Australia Pat. Appl. No.2016900158 filed on Jan. 19, 2016, each of which is incorporated in itsentirety by reference herein.

BACKGROUND Field

This invention generally relates to Magnetic Resonance Imaging. Morespecifically, the invention relates to radio-frequency magnetic fieldpulse sequences and associated magnetic field gradients.

Description of the Related Art

Magnetic Resonance Imaging (MRI) exploits the nuclear magnetic resonance(NMR) phenomena by combining NMR with gradient magnetic fields to allowcross-sectional slice-selective excitation of nuclei within a subjectunder examination. Typically, a pulse-sequence of radio-frequencymagnetic fields (RF pulse) and associated magnetic field gradients isused with further two dimensional (2D) encoding of the NMR signals tocreate a 2D image of a portion of the subject. A 3D image of the subjectcan then be obtained by combining many slices together.

By increasing the static magnetic field strength (B0) an improvedsignal-to-noise ratio may be obtained along with improved spatialresolution in the images created. Ideally, in an MR system the RF pulseshould deliver a defined rotation of the nuclear magnetization vector α°to provide uniform signal strength over the dimensions of the sample.However, local magnetic and electrical field effects in the subject canlead to spatial inhomogeneity in the local radio-frequency (RF)transverse magnetic field (B1) the nuclei are exposed to. This affectsimaging as the MM pulse sequence employed may not result in the intendedrotation of the nuclear magnetisation vector (M). Inhomogeneity in theB1 field is more problematic at B0 fields above 3 T and can lead toimaging artefacts which, in the worst case, are manifested as zerosignal in some regions of the image. B1 inhomogeneity effects may alsooccur at low or medium B0 fields, and when inhomogeneous RF coils suchas surface coils are used.

These problems can be addressed by using a multiplicity of transmitcoils and activating them in a particular manner to attempt to generatea uniform B1 field. However the manner of activation cannot bepre-computed and must be calculated in real time while the subject ispositioned in the imaging device and stationary. Moreover thecalculations can take many minutes to complete, and while they areoccurring the patient cannot move.

Reference to any prior art in the specification is not an acknowledgmentor suggestion that this prior art forms part of the common generalknowledge in any jurisdiction or that this prior art could reasonably beexpected to be understood, regarded as relevant, and/or combined withother pieces of prior art by a skilled person in the art.

SUMMARY

In order to address the drawbacks noted above, the present inventorshave developed methods that can be implemented without the need forextensive real-time calculations. Most preferably they can beimplemented in MM systems using a single transmit coil.

Preferred embodiments use a Mill pulse sequence that aim, in total, tocause a desired total rotation of the net magnetisation vectorrepresenting a resultant magnetisation of the nuclear magnetic momentsof an ensemble of nuclei in the portion of the subject. The pulsesequence involves a plurality of slice selective pulses which eachindividually have a desired rotation that is less than or equal to thetotal desired rotation. The slice selective pulses each cause a rotationabout respective axes, which may be different to each other. In someembodiments, successive rotations are performed about alternating axes.In some forms the axes are orthogonal to each other. Optionally phasecorrection (re-phasing) gradients can also be included in the pulsesequence.

In a first aspect of the present invention, there is provided a methodfor use in magnetic resonance imaging including: exposing at least aportion of a subject to a longitudinal magnetic field (B0) such that anet magnetisation vector representing a resultant magnetisation of thenuclear magnetic moments of an ensemble of nuclei in the portion of thesubject, is longitudinally aligned with the magnetic field (B0);performing a first slice-selective rotation by exposing at least saidportion of the subject to a first radio-frequency magnetic field pulse(B1a) and a corresponding first magnetic field gradient to excite nucleiwithin the portion subject, the first radio-frequency magnetic fieldpulse being configured to rotate the net magnetisation about a firstaxis by a first angle such that a first component of the netmagnetisation lies in a first plane including the first axis and asecond component of the net magnetisation remains aligned with themagnetic field (B0); performing a second slice-selective rotation byexposing at least said portion of the subject to a secondradio-frequency magnetic field pulse (B1b) and corresponding secondmagnetic field gradient to excite nuclei within the portion of thesubject, the second radio-frequency magnetic field pulse beingconfigured to rotate the net magnetisation about a second axis by asecond angle such that at least a portion of the net magnetisation thatremained aligned with the magnetic field (B0) after the first sliceselective rotation lies in a plane including the second axis ofrotation; and performing a final phase adjustment by exposing at leastsaid portion of the subject to a final re-phasing magnetic fieldgradient to correct de-phasing of the magnetisation vectors within theensemble that exist after the second slice-selective rotation.

In some cases additional slice selective rotations can be performed. Insome embodiments a third slice-selective rotation can be performed byexposing at least said portion of the subject to a third radio-frequencymagnetic field pulse (B1c) and a corresponding third magnetic fieldgradient to excite nuclei within the portion of the subject, the thirdradio-frequency magnetic field pulse being configured to rotate the netmagnetisation about the first axis by a third angle; and the final phaseadjustment is performed after the third slice selective rotation.

In a second aspect of the present invention, there is provided a methodfor use in magnetic resonance imaging including: exposing at least aportion of the subject to a longitudinal magnetic field (B0) such that anet magnetisation vector representing a resultant magnetisation of thenuclear magnetic moments of an ensemble of nuclei in the portion of thesubject, is longitudinally aligned with the magnetic field (B0);performing a first slice-selective rotation by exposing at least saidportion of the subject to a first radio-frequency magnetic field pulse(B1a) and a corresponding first magnetic field gradient to excite nucleiwithin the portion subject, the first radio-frequency magnetic fieldpulse being configured to rotate the net magnetisation about a firstaxis by a first angle such that a first component of the netmagnetisation lies in a first plane including the first axis and asecond component of the net magnetisation remains aligned with themagnetic field (B0); performing a first phase adjustment by exposing atleast said portion of the subject to a first re-phasing magnetic fieldgradient to correct de-phasing of magnetisation vectors within theensemble that is a result of the first slice-selective rotation, and toover-correct said de-phasing of the magnetisation vectors within theensemble; performing a second slice-selective rotation by exposing atleast said portion of the subject to a second radio-frequency magneticfield pulse (B1b) and corresponding second magnetic field gradient toexcite nuclei within the portion of the subject, the secondradio-frequency magnetic field pulse being configured to rotate the netmagnetisation about a second axis by a second angle such that at least aportion of the net magnetisation that remained aligned with the magneticfield (B0) after the first slice selective rotation lies in a planeincluding the second axis of rotation; and performing a final phaseadjustment by exposing at least said portion of the subject to a finalre-phasing magnetic field gradient to correct de-phasing of themagnetisation vectors within the ensemble that is a result of the secondslice-selective rotation.

In some cases additional slice selective rotations can be performed. Insome embodiments a third slice-selective rotation can be performed byexposing at least said portion of the subject to a third radio-frequencymagnetic field pulse (B1c) and a corresponding third magnetic fieldgradient to excite nuclei within the portion of the subject, the thirdradio-frequency magnetic field pulse being configured to rotate the netmagnetisation about the first axis by a third angle.

In a third aspect of the present invention, there is provided a methodfor use in magnetic resonance imaging including exposing at least aportion of the subject to a longitudinal magnetic field (B0) such that anet magnetisation vector representing a resultant magnetisation of thenuclear magnetic moments of an ensemble of nuclei in the portion of thesubject, is longitudinally aligned with the magnetic field (B0);performing a first slice-selective rotation by exposing at least saidportion of the subject to a first radio-frequency magnetic field pulse(B1a) and a corresponding first magnetic field gradient to excite nucleiwithin the portion of the subject, the first radio-frequency magneticfield pulse being configured to rotate the net magnetisation about afirst axis by a first angle such that a first component of the netmagnetisation lies in a first plane including the first axis and asecond component of the net magnetisation remains aligned with themagnetic field (B0), and wherein within the portion of the subject thefirst magnetic field gradient results in a magnetic field with amagnitude that increases along a first gradient direction; performing asecond slice-selective rotation by exposing at least said portion of thesubject to a second radio-frequency magnetic field pulse (B1b) andcorresponding second magnetic field gradient to excite nuclei within theportion of the subject, the second radio-frequency magnetic field pulsebeing configured to rotate the net magnetisation about a second axis bya second angle such that at least a portion of the net magnetisationthat remained aligned with the magnetic field (B0) after the first sliceselective rotation lies in a plane including the second axis ofrotation, and wherein the second magnetic field gradient results in amagnetic field with a magnitude that decreases along the first gradientdirection and at least partly re-phases a de-phasing of themagnetisation vectors within the ensemble that is a result of the firstslice-selective rotation.

In some forms the present invention provides a method in an MRI systemand magnetic resonance imaging pulse that includes three components.Most preferably the first and third components induce a rotation in thesame direction, while the second induces a rotation in a different(preferably orthogonal direction).

The pulse sequence has a desired net rotation, but the summed desiredrotation of its components are greater than the desired net rotation.For example in a case where a desired net rotation is 180 degrees thecomponents can be 90 degree rotations, and the summed desired rotationsof its components are 270 degrees.

In a fourth aspect of the invention there is provided a method for usein magnetic resonance imaging including exposing at least a portion of asubject to a longitudinal magnetic field (B0) such that a netmagnetisation vector representing a resultant magnetisation of thenuclear magnetic moments of an ensemble of nuclei in the portion of thesubject, is longitudinally aligned with the magnetic field (B0);performing a first slice-selective rotation by: exposing at least saidportion of the subject to a first radio-frequency magnetic field pulse(B1a) and a corresponding first magnetic field gradient to excite nucleiwithin the portion subject, the first radio-frequency magnetic fieldpulse being configured to rotate the net magnetisation about a firstaxis by a first angle such that a first component of the netmagnetisation lies in a first plane including the first axis and asecond component of the net magnetisation remains aligned with themagnetic field (B0); performing a second slice-selective rotation by:exposing at least said portion of the subject to a secondradio-frequency magnetic field pulse (B1b) and corresponding secondmagnetic field gradient to excite nuclei within the portion of thesubject, the second radio-frequency magnetic field pulse beingconfigured to rotate the net magnetisation about a second axis by asecond angle such that at least a portion of the net magnetisation thatremained aligned with the magnetic field (B0) after the first sliceselective rotation lies in a plane including the second axis ofrotation; and performing a third slice-selective rotation by: exposingat least said portion of the subject to a third radio-frequency magneticfield pulse (B1c) and a corresponding third magnetic field gradient toexcite nuclei within the portion of the subject, the thirdradio-frequency magnetic field pulse being configured to rotate the netmagnetisation about the first axis by a third angle.

In a fifth aspect of the present invention, there is provided a magneticresonance imaging (MM) system including: magnetic field producing meansfor producing a magnetic field (B0); magnetic field gradient producingmeans configured to produce magnetic field gradients to alter themagnetic field B0 and produce an effective magnetic field;radio-frequency magnetic field generating means configured to produceradio-frequency magnetic fields (B1a and B1b); and positioning means forpositioning at least part of a subject to be exposed to the effectivemagnetic field; wherein the system is configured to perform any one ofthe methods disclosed herein.

In other aspects of the present invention, there are provided magneticresonance imaging (MRI) pulse sequences to be used with a magneticresonance imaging system. The pulse sequences may be used by any one ofthe methods disclosed herein.

As noted above inhomogeneity in the B1 field is more problematic at B0fields above 3 T, however application of the various aspects andembodiments of the present invention should not be considered to belimited to this field strength. Aspects and embodiments can findapplication at lower B0 levels, e.g. 1.5 T and above or perhaps lower.This is particularly the case for aspects or embodiments which increasethe level of useable signal obtained from the MRI system.

As used herein, except where the context requires otherwise, the term“comprise” and variations of the term, such as “comprising”, “comprises”and “comprised”, are not intended to exclude further additives,components, integers or steps.

Further aspects of the present invention and further embodiments of theaspects described in the preceding paragraphs will become apparent fromthe following description, given by way of example and with reference tothe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a magnetic resonance imaging system;

FIG. 2a is a vector diagram showing the equilibrium net magnetisationfrom an ensemble of nuclei in a uniform magnetic field B0;

FIG. 2b illustrates a pair of vector diagrams, the leftmost being athree dimensional diagram, and the rightmost being a projection onto they-z plane, each a first rotation of the net magnetisation when theensemble of nuclei are excited by a suitable RF magnetic field;

FIG. 2c illustrates a pair of vector diagrams, the leftmost being athree dimensional diagram, and the rightmost being a projection onto thex-z plane, each showing a second rotation of the net magnetisation whenthe ensemble of nuclei are excited by a suitable RF magnetic field;

FIG. 3 is a plot of the magnitude of the residual magnetisationcomponents along the x-, y- and z-axes for a range of firstrotation/pulse angles;

FIG. 4 is a plot of an exemplary MRI pulse sequence;

FIG. 5a is a plot of magnetic field strength as a function of positionwith gradient applied;

FIG. 5b is a plot of Larmor frequency as a function of position withgradient applied;

FIG. 6a illustrates a series of vector diagrams of the magnetisation atdifferent z positions, denoted as z₊, z₀ and z⁻, within a slice (whereslice selection along the z-axis is being applied) after rotation by afirst RF magnetic field to schematically illustrate dephasing thatoccurs at different z positions within the slice; a correspondingprojection onto the x-y plane is also illustrated;

FIG. 6b is a series of vector diagrams corresponding to FIG. 6a butschematically illustrates the phase correction process across the widthof the selected slice in the z direction;

FIG. 6c illustrates a further series of vector diagrams of themagnetisation at different z positions within the slice andschematically illustrates the phases after the over-correction of phaseswithin a slice by a first re-phasing gradient; a correspondingprojection onto the x-y plane is also provided;

FIG. 7 is a plot of magnetic field strength as a function of positionwith a reversed polarity gradient applied;

FIG. 8a illustrates three plots showing the residual magnetism in eachof the x, y and z directions using an embodiment of the presentinvention;

FIG. 8b illustrates three plots showing the residual magnetism in eachof the x, y and z directions as a result of a single 45° rotation;

FIGS. 9a to 9e illustrate results using an embodiments of the presentinvention;

FIG. 10 illustrates another embodiment of an MM pulse sequence accordingto an aspect of the present invention which uses a second sliceselective gradient that performs re-phasing of spin vectors as well asslice selection;

FIG. 11 illustrates another embodiment of an MM pulse sequence accordingto an aspect of the present invention that uses three pulses in two axesof rotation to generate a slice selective 180 degree refocussing pulseor an inversion pulse when the initial magnetisation starts along the +zaxis;

FIGS. 12a to 12d schematically illustrate the rotations of the netmagnetisation when the pulse sequence of FIG. 11 is used as a sliceselective 180 degree refocussing pulse;

FIGS. 13a and 13b respectively illustrate a simulation of the operationof a conventional 180 degree refocussing pulse (FIG. 13a ) and asimulation of the operation of a pulse sequence of FIG. 11 (FIG. 13b );

FIGS. 14a to 14d schematically illustrate the rotations of the netmagnetisation when the pulse sequence of FIG. 11 is used as an inversionpulse;

FIG. 15 illustrates an alternative MRI pulse sequence equivalent to thatof FIG. 11, but which uses no dedicated re-focussing gradients;

FIGS. 16a and 16b illustrate simulations of the operation of aconventional inversion pulse (FIG. 16a ) compared to that of the 180degree inversion pulse (FIG. 16b ) sequence of similar structure to thatof FIG. 11;

FIG. 17 illustrates another embodiment of an MM pulse sequence accordingto an aspect of the present invention that uses three pulses in two axesof rotation to generate a 90 degree excitation pulse;

FIG. 18 illustrates an alternative MRI pulse sequence equivalent to thatof FIG. 17 to generate a 90 degree excitation pulse;

FIGS. 19 and 20 respectively illustrate simulations of the operation ofa conventional 90 sinc excitation pulse (FIG. 19) and simulations of theoperation of the three component 90 degree excitation pulse of FIG. 17(FIG. 20);

FIG. 21 illustrates simulations of the total received signal strength,for a conventional 90 degree sinc pulse and several exemplary 90 degreepulse sequences of the present invention, plotted over a range of RFsignal amplitudes;

FIG. 22 illustrates simulations of the total received signal strength,for a conventional 180 degree sinc inversion pulse and a three-component180 degree inversion pulse sequence of the present invention, plottedover a range of RF signal amplitudes; and

FIG. 23 illustrates simulations of the total received signal strength,for a conventional 180 degree sinc refocussing pulse and athree-component 180 degree refocussing pulse sequence of the presentinvention, plotted over a range of RF signal amplitudes.

DETAILED DESCRIPTION

FIG. 1 shows a highly schematic block diagram for a Magnetic ResonanceImaging (MRI) system 10 including:

a magnetic field producing means 20;

a magnetic field gradient producing means 30;

a radio-frequency magnetic field generating means 40;

an RF receiver 46;

a positioning means 50; and

a control unit 70.

The magnetic field producing means 20 is configured to produce a staticuniform magnetic field B0,s, 22 aligned to a longitudinal directionalong the z-axis (FIG. 2a ). A preferred example of the field producingmeans 20 is a superconducting magnet system.

The magnetic field gradient producing means 30 is configured to producea magnetic field gradient G, 32. This can be thought of an additionalmagnetic field that alters the magnetic field B0,s to produce a modifiedmagnetic field B0, 24. The gradient is not strong enough to vary thedirection of the field, so B0 is always parallel with B0,s in thelongitudinal axis. Therefore it suffices to define B0 in terms of thecomponent in the longitudinal direction and it is unnecessary to referto it as a vector quantity. It will therefore be referred to as a scalarquantity B0 without loss of generality. As will be discussed furtherbelow, the gradient is used for slice selection.

The radio-frequency (RF) magnetic field generating means 40 isconfigured to produce transversely oriented RF magnetic fields B1a andB1b, i.e. oriented such that they lie in the x-y plane, that oscillateat a radio-frequency corresponding to the Larmor frequency of a nucleiof interest for MRI (typically protons or carbon-13) exposed to themagnetic field B0. The RF magnetic fields may be linearly or circularlypolarised depending on the type of RF magnetic field generating means 40used and have a phase defined by the operator.

The positioning means 50 is for positioning at least part of a subject60 in the magnetic field B0.

The system also includes a RF receiver 46, such as RF receiver coils,for receiving an MRI signal. In some embodiments, the RF receiver ispart of the RF magnetic field generating means 40. The RF receiver istypically only sensitive to RF magnetic fields oriented in thetransverse plane.

In some embodiments, the system 10 includes a control unit 70. Controlunit 70 is communicatively coupled with the other components (20, 30,40, 50) of the system 10. Control unit 70 may include a storage means 72for storing instructions that determine how the control unit 70 controlsthe other components (20, 30, 40, 50). Instructions include programs forgenerating MM pulse sequences that vary the RF magnetic fields B1 andthe magnetic field gradient G to selectively excite nuclei in across-sectional slice of the subject exposed to the magnetic field B0.By varying the gradients over two dimensions in k-space, the MM signalscan be spatially encoded to produce a 2D raw image (phase encoding,frequency encoding). Using known Fourier transform MM techniques, the 2Draw image can be converted or transformed into a 2D image of across-sectional slice of the subject. Careful selection of pulsesequence parameters can be used to improve image contrast betweenvarious compounds or materials within the subject. By taking many 2Dimages a 3D image of the subject can be obtained.

The magnetic field producing means 20 may either be controlled by thecontrol unit 70 or it may be persistently producing field B0 (as isusually the case for a superconducting magnet system). The magneticfield producing means 20 and magnetic field gradient producing means 30may also be in communication with the control unit 70 such that thecontrol unit can monitor their status and/or functionality. For example,the control unit 70 may monitor whether the correct magnetic fieldstrength is being produced, either directly through measuring the protonfrequency of the signal from water or indirectly by monitoring anelectrical characteristic of the field producing means 20 such as poweroutput.

The subject 60 contains an ensemble of nuclei each with a magneticmoment. When at least a portion of the subject 60 (therefore theensemble of nuclei within the portion) is exposed to the magnetic fieldB0 it is considered that, statistically, a greater proportion of thenuclei's magnetic moments become aligned with the magnetic field B0. Thetime-averaged magnetisation of the portion exposed to the magnetic fieldB0 is, at equilibrium, described by a net magnetisation vector M, 24parallel to the direction of the magnetic field B0 (FIG. 2a ). At thestart of an MRI pulse sequence, the magnetisation M is considered to beat equilibrium and oriented as shown in FIG. 2 a.

As will be appreciated by the person skilled in the art, exposure of asubject to a magnetic field is not intended to be limited to meanexposure of a surface of the subject, or the near sub-surface, and isintended to include exposing the nuclei within and throughout thesubject to said magnetic field. The use of the term is also intended toinclude the situation where the MM system has a persistent magneticfield B0 and the subject is introduced into the field.

Rotation of Magnetisation Vector by RF Magnetic Fields

As is known in the art, a transverse RF magnetic field (B1) that isorthogonal to the main magnetic field B0 is typically used to causerotation of the net magnetisation M, 24 away from the longitudinal axis(z-axis) so that a component of magnetization is created in thetransverse plane. This is necessary for the RF receivers to measure aMRI signal. Typically, a 90° rotation is desired to completely rotate orflip the magnetisation into the transverse plane to maximise the MRIsignal.

As illustrated in FIGS. 2b and 2b , in an embodiment of the invention,an MM sequence with two RF oscillating magnetic fields (B1a and B1b) isused to rotate the magnetisation vector M from its initial alignment inthe z-direction towards (or close to) a transverse plane 80 (the x-yplane that is orthogonal to the z-axis).

FIG. 2b shows in its leftmost figure a three dimensional representationof a magnetisation M, and in its rightmost figure a projection of thisrotation onto the y-z plane, to aid visualisation. In this example, thefirst RF magnetic field (B1a) excites the nuclei and causes a firstrotation of the magnetisation M about a first axis (which is defined asthe x-axis) by a first angle (θ1) towards the y-axis and thereforetowards the transverse plane 80. As the magnetisation M is rotated awayfrom its original equilibrium orientation 24 aligned with the z-axis,the rotated magnetization 25 can be considered to consist of atransverse vector component (Mt, 25 a) in the x-y plane 80 and aresidual vector component (z-component) aligned along the z-axis (Mz, 25b). The z-component Mz may be parallel or anti-parallel to the z-axisdepending on the magnitude of the first angle θ1. As the ensemble isstill exposed to the magnetic field B0, the transverse component Mt (andtherefore the rotated magnetisation, M) precesses about the z-axis atthe Larmor frequency. The magnetisation vectors shown in the drawingsare drawn in the rotating frame of reference rotating at the Larmorfrequency.

The desired first angle of rotation θ1 can be set by choosing anappropriate combination of duration and amplitude of a pulsed RFmagnetic field B1a. As noted above, parts of the subject being scannedmay affect the local strength of the RF magnetic fields (B1) atparticular locations (spatial inhomogeneity) and cause the correspondingrotation angle at said locations to also be affected. This may result inup to a 50% variation in the actual rotation angle compared to the setangle, i.e. for a 90° rotation angle, this could result in an actualrotation between 45° and 135°.

The present inventor has identified that by exposing the subject to asecond slice-selective RF magnetic field B1b that is configured torotate the magnetisation about an orthogonal axis in the rotatingreference frame (or in the case of circularly polarised RF magneticfields, that is 90° out of phase with the first RF field B1a), portionsof the subject where the rotation angle deviates from the set angle canbe further rotated closer to or into the transverse plane. This isfurther explained in an exemplary embodiment with regard to FIG. 2 c.

As shown in FIG. 2c , the second RF magnetic field (B1b) excites theensemble of nuclei to induce a second rotation of the rotatedmagnetisation M in orientation 25 about a second axis, in this examplethe y-axis (therefore orthogonal to the first axis), by a second angle(θ2) towards the transverse plane 80 to a second orientation 26.

The second rotation can be considered as only rotating the residualcomponent of magnetization Mz 25 b towards the transverse plane 80 asthe transverse component Mt 25 a is aligned with the y-axis. Notably, ifthe effect of the first rotation was to rotate the magnetisation by 90°into the transverse plane 80 then there is no further rotation by thesecond RF magnetic field.

The second angle θ2 can be selected in the same manner as the firstangle. In a preferred embodiment, the second angle θ2 is set to be twicethat of the first angle θ1. Importantly, the spatial inhomogeneity ofthe first RF magnetic field does not vary greatly with direction of theapplied RF field and therefore will have the same effect on the secondRF magnetic field B1b and therefore the corresponding rotation angle.The ratio between the first and second angles can therefore be set. Forexample, if the desired first and second angles are set at 90° and 180°respectively, and the first rotation angle was reduced to 45°, then thesecond rotation will be 90°. This still results in a magnetisationvector that is in the transverse plane. The same holds true ifinhomogeneity causes over-rotation by 50% and results in first andsecond angles of 135° and 270°. Notably, the magnetisations are alsorotated such that the phase differences (in terms of orientation betweenthe components in the transverse plane) can be 45° from a single 90°rotation. Furthermore, the rotation following first and second angles of135° and 270° results in a magnetisation that is 90° out of phase withsomething that was rotated by first and second angles of 45° and 90°.

If the resultant rotation at some portion of the subject is at otherintermediate angles (i.e. between 45° and 135°) as is the caseillustrated in FIGS. 2b and 2c , the resultant magnetisation vectorafter the two part rotation due to the first and second RF magneticfields can be shown to still be close to the transverse plane. In otherwords, a larger component of the magnetisation vector is in thetransverse plane compared to the residual component aligned with thelongitudinal axis.

The resultant magnetisation at a given point in the slice, after a twopart rotation where the ratio between first and second angle is 1:2 maynot always be closer to the transverse plane than the situation whereonly one rotation is performed. However, the result from two partrotation is more uniformly close to the transverse plane over a largerrange of angles than if only one rotation is performed. In this way, thetwo part rotation is less sensitive to inhomogeneity in the RF magneticfield B1. Simulated results illustrating the operation of an embodimentare shown in FIG. 3.

FIG. 3 illustrates 6 groups of plots, with each group labelled 0.5,0.75, 1.0, 1.25, 1.35 or 1.5. The numerical label given to each group(e.g. 0.5) indicates the extent of the influence of B1 inhomogeneity onthe level of desired rotation illustrated in each group of plots. Thatis, the group of plots labelled 0.5 shows the simulated resultantmagnetisation in the x direction (top plot—Mx), y direction (centreplot—My) and z direction (bottom plot—Mz) when the B1 inhomogeneityreduces the actual rotation caused by an MRI pulse to half of theintended (or desired) rotation. Similarly the plot labelled 1.5 showsthe simulated residual magnetisation in the x, y and z direction whenthe local effect of B1 (caused by the B1 inhomogeneity) increases theactual rotation by 50% over that desired. In each case, the graphsillustrate the simulated residual magnetisation after a pulse containingtwo orthogonal slice selective rotations that have relative rotation of0.8:1 e.g. 72°:90°. However, other relative rotation ratios may alsowork as discussed herein.

As can be seen in each of the six groups of plots, the residualmagnetisation at the centre of the slice, i.e. the point on the plotswhere position (mm) is 0, is almost zero in the z direction (bottomplot), indicating that the resultant magnetisation is almost entirely inthe x-y plane.

As can be appreciated by the person skilled in the art, the first andsecond rotation axes are preferably orthogonal.

Slice Selection

In addition to the RF magnetic fields B1a and B1b, the MRI sequenceincludes a magnetic field gradient to perform slice-selective rotation.A time sequence of the amplitudes of the RF magnetic field and magneticfield gradients is shown in FIG. 4 and an alternative embodiment isshown in FIG. 10. The pulse sequence of FIG. 4 includes:

-   -   a first slice selective rotation, generated by first RF pulse 51        and corresponding first magnetic field gradient 52;    -   a second a slice selective rotation, generated by a second RF        pulse 55 and corresponding second magnetic field gradient 54;        and    -   one or more phase adjustments; in this case being, a final        re-phasing of de-phased magnetisations performed by application        of a final re-phasing magnetic field gradient 56, and a first        phase adjustment that is performed before the second slice        selective rotation by application of a first re-phasing gradient        53.

In an exemplary embodiment where an axial cross-section is desired, alinear gradient along z is used so that the field at a position z isgiven by:B ₀(z)=|B ₀ |G _(z)

FIG. 5a shows the magnetic field strength B0 as a function of positionalong z with a positive magnetic field gradient G that varies along thez-direction. As can be seen, the magnetic field is higher at larger zand lower at smaller z and equal to the magnitude of B0 with zerogradient. As the Larmor frequency (ω) is proportional to the magneticfield strength, the Larmor frequency of nuclei in the portion of thesubject exposed to the magnetic field gradient also varies along thez-direction (FIG. 5b ). As is known in the art, the magnetic fieldgradient is used to select an axial slice of the subject (from Z− to Z+)to excite the nuclei therein with the transverse RF magnetic fields. Inthe embodiments described herein, only the nuclei within the slice areexcited by RF magnetic fields B1a and B1b that cause rotation of the netmagnetisation about x and y axes respectively. This is further explainedbelow.

Slice selection is made possible by using RF magnetic fields that areamplitude modulated with functions known in the art to produce magneticfields with a restricted bandwidth of frequencies. As an example, if theRF magnetic field is modulated as a ‘sinc’ function in time, the Fouriertransform of this leads to a rectangular function in frequency.Therefore, RF magnetic fields with a finite bandwidth of frequenciesover the range covered by the rectangular function can selectivelyexcite a portion of the subject with a corresponding Larmor frequencywithin this frequency bandwidth (See FIG. 5b ).

In this example the gradients applied at the time of the B1a and B1bfields have the same amplitude and B1a and B1b overlap in frequenciescovered, the same selected slice of the ensemble of nuclei in thesubject is excited by both B1a and B1b. As will be seen FIG. 10 shows analternative approach in which the slice selection gradients provide amagnetic field that changes magnitude in opposite directions, that isone of the slice selection gradients has a positive gradient and theother a negative gradient.

As previously discussed, in a preferred embodiment, the second rotationangle is twice that of the first angle. This could be achieved if thepulse length of B1b is twice that of B1a, or the amplitude of B1b isdoubled that of B1a, or a suitable combination of pulse length andamplitude adjustment is used. In other embodiments, B1a and B1b areeither identical or the ratio of the B1a pulse length to the B1b pulselength can be any suitable ratio.

In practical embodiments, the RF magnetic fields are limited in time,commonly referred to as RF pulses. In preferred embodiments, the RFmagnetic field is modulated as a time-limited sinc function (See FIG.4). This can be considered a sinc function multiplied by a windowfunction such as a Hamming, rectangular function or any known windowfunction.

The person skilled in the art will appreciate that a magnetic fieldgradient G varying along different axes can be used to select slices indifferent orientations. For example G can vary along a transverse axisto produce sagittal or coronal slices of the subject.

Phase Adjustment

Any given group of nuclei exposed to the same magnetic field B can bedescribed by a single net magnetisation vector M. As discussed earlier,the gradients do not alter the field direction but, as shown in FIG. 5b, the Larmor frequency varies with position when a gradient is present.After the first RF magnetic field B1a rotates the magnetisation vector Mto orientation 25 the magnetisation vector M at a particular positionalong the z-axis precesses about the z-axis at the Larmor frequencycorresponding to that position. According to FIG. 5b , the magnetisationvector at positions higher than position z0 (M_(z+)) will precess fasterthan the magnetisation at z0 (M_(z0)) due to the higher strengthmagnetic field B0 at that position along the z-axis. The magnetisationat lower positions (M_(z+)) precess slower than that at z0 due to thelower strength magnetic field B0. With reference to FIG. 6a , the resultof gradient 52 is that the magnetisation vectors begin de-phasing withrespect to the magnetisation at z0 during pulse 52. The amount ofde-phasing can be quantified by a phase angle φ between themagnetisation at either end of the slice with respect the magnetisationat z0. FIG. 6a illustrates a series of vector diagrams of themagnetisation at different z positions, denoted as z₊, z₀ and z⁻, withina slice, after rotation by a first RF magnetic field to schematicallyillustrate dephasing that occurs at these three different z. Aprojection of the phases of M_(z+), M_(z0) and M_(z−) is provided as thelower plot. FIG. 6a shows the magnetisation at time “a” during the MRIpulse sequence as shown in FIG. 4. As can be seen the phase at positionz+ is advanced by a phase angle of φ compared the phase at z0, indicatedby +φ on the topmost plot in FIG. 6a . Conversely the phase at positionz− lags by a phase angle of φ compared the phase at z0, and is indicatedby −φ on the lower plot of FIG. 6 a.

As will be known by those skilled in the art it is important to re-phasethe magnetisation vectors within the portion to obtain a larger MMsignal.

The phase can be adjusted in a first phase adjustment. This can beachieved by applying a re-phasing gradient with a polarity that isreversed with respect to the first slice selection gradient. For examplea re-phasing magnetic field gradient 53 as shown in FIG. 7 can beapplied. The re-phasing gradient produces a lower strength magneticfield at higher positions along the z-axis and higher strength magneticfields at lower positions.

FIG. 6b shows a series of vector diagrams corresponding to FIG. 6a butschematically illustrates the phase correction process across the widthof the selected slice in the z direction. Approximate re-phasing occurswhen this negative gradient has been applied for half the(time×magnitude) integral area of the gradient applied in conjunctionwith the first slice selection pulse. This completes the normal sliceselection process. However, in accordance with some embodiments thephase correction process does not end when the phase at positions z+ andz− are the same as phase at z0 (i.e. when fully re-phased) but insteadthe phase is over corrected, such that the phase at position z+ lags bya phase angle of φ the phase at z0, indicated by −φ on the topmost plotin FIG. 6b , and also the phase at position z-leads by a phase angle ofφ compared the phase at z0, and is indicated by +φ on the lower plot ofFIG. 6b . Thus the phase at position z+ is retarded by 2φ angle asindicated by reference number 41 and the phase at position z− isadvanced by 2φ angle as indicated by reference number 42.

FIG. 6c illustrates a further series of vector diagrams of themagnetisation at different z positions within the slice andschematically illustrates the phases after the over-correction ofphases. FIG. 6c illustrates the final phases of M_(z+), M_(z0) andM_(z−) at locations z+, z0 and z− respectively. The magnetisation vectorMz+(at positions higher than position z0) now precess slower than themagnetisation at z0 and the magnetisation M− (at lower positions)precess faster than that at z0. A corresponding projection onto the x-yplane is also provided.

At some time during the application of the second slice-selectiongradient 54, the magnetisation may be, or be close to being, completelyin-phase. However during the second slice-selective rotation they willagain de-phase.

Accordingly, following the second slice-selective rotation of themagnetisation by the second RF magnetic field 55 (B1b), themagnetisation at different z positions are again de-phased. A finalphase adjustment is applied by using a reversed gradient in a finalre-phasing magnetic field 56 to correct the de-phasing within theensemble. This final phase adjustment is applied to re-phase themagnetisation vectors within the ensemble so that they are in-phase tomaximise the MM signal.

The lower plot of FIG. 4, illustrates the phase of the magnetisationvectors at positions higher (z+) than z0, and the phase of themagnetisation vectors at positions lower (z−) than z0, as a function oftime to illustrate schematically the evolution of phase during theapplication of the pulse sequence. The phase evolution can berepresented by a plot in which phase effectively originates from zero atthe middle of any RF pulse element, where the final phase accumulatedafter successive gradient pulse elements is accumulative. Re-phasing ofthe signal excited across the selected slice occurs at all points wherethe net phase is zero.

In the lower plot of FIG. 4 the phase evolution generated by the firstslice selective pulse 51 is indicated by reference number 51′ and shownin the lower plot marked with crosses. The second RF pulse 55 andrephasing gradients 53 and 56 each affect their own signals that evolvefrom the centre of each pulse. The phase evolution of the second RFpulse 55 is labelled by reference numeral 55′ shown in the lower plotmarked with paired dashes. Thus the two component RF pulse sequence ofthe present embodiment thus excites two signals, both of which providemaximum signal at a subsequent point in time when the net phaseaccumulation from both signals are simultaneously zero. The phases ofthe signals are along the x- and y-transverse directions as effected bythe different phases of the two pulses (x- and y-) so that the netsignal has a phase formed by the vector-sum of the two components.

In the embodiment shown in FIG. 4, the first re-phasing gradient 53 hasa larger amplitude than the first slice-selective gradient 52. Also, theintegral of the amplitude of the first magnetic field gradient 52 overtime is equal to the integral of the amplitude of the first re-phasingmagnetic field gradient 53 over time. In some embodiments, the firstre-phasing gradient also has a shorter duration than the firstslice-selective gradient.

It should be noted that the figure is schematic insofar as it does notshow the precise shape of the phase evolution curve over time and allslice-selective signal excitation pulses have a non-symmetric gradientprofile since they must contain the extra-refocusing element required toaccount for magnetization evolution during the RF period. In a preferredembodiment, the ratio between the magnitude of the first re-phasingmagnetic field gradient is above 2 and typically between 2.02 and 2.04times the magnitude of the first magnetic field gradient. In a mostpreferred embodiment, the ratio between the magnitude of firstre-phasing magnetic field gradient and the first magnetic field gradientis 2.03. The final orientations of the net magnetisation at differentpositions along the z-axis after a MM pulse sequence in accordance withthe disclosed invention have been calculated by solving the Blochequations and shown in FIG. 8a . A ratio of 2.03 was used for thecalculation. The plot shows the magnitude of the components of the finalmagnetisation along each orthogonal axis. Although there is somevariation at different positions along the z-axis, the residualcomponent aligned with the z-axis is very small compared to thecomponents aligned with the x and y axes. As the x and y components havea similar magnitude at different positions along the z-axis, the plotalso indicates that the de-phased magnetisations are now mostly in-phaseand the de-phasing has been largely corrected. That is, FIG. 8a showsthat at all positions along z, the magnetisation is close to or at a 45°angle between the x and y axis. This phase correction is largely due tothe selection of a ratio of 2.03 between the magnitude of firstre-phasing magnetic field gradient and the first magnetic fieldgradient.

As a comparison to the result of the MM sequence described above, FIG.8b shows the result of a single 45° rotation. This illustrates theresult of an inhomogeneity reducing the rotation angle of an intendedsingle 90° rotation by 50%. It can be seen in FIG. 8b that there is astill a significant magnitude to the Mz component.

FIGS. 9a to 9e illustrate additional results using embodiments of thepresent invention. Specifically FIG. 9a illustrates a gradient echo MMof a uniform spherical phantom using a standard 90° sinc pulse. As canbe seen the signal level varies greatly across the slice, and has adistinct dark central patch. The bright scalloped edges correspond tolocal inhomogeneity caused in areas near to the transmit coils. FIG. 9billustrates an image of the same phantom using a 1-2 pulse sequence,such as that illustrated in FIG. 4. In the pulse used a first 45° sliceselective rotation in the x direction is followed by a second 90° sliceselective rotation in the y direction. As can be seen qualitatively theimage in FIG. 9b is more uniform than that of FIG. 9 a.

FIGS. 9c and 9d illustrate RF flip angle maps corresponding to FIGS. 9aand 9b . In each figure, the arrows indicate a correlation between theflip angle scale on the right and shading in the RF flip angle map. Ascan be seen, in FIG. 9c , the flip angle in the centre of the phantomare past 90 degrees, and is surrounded by a ring of flip angles of 60degrees and below. In FIG. 9d the flip angles are far more uniform andthe vast majority sit in a narrow angular range about the desired 90°.This view is further supported by FIG. 9e which illustrates the flipangle distribution for the conventional 90° sinc pulse (solid blue,labelled 91) and equivalent 1-2 pulse sequence (dashed, red line,labelled 92). The improved flip angle homogeneity can be seen in 9 e bythe tightness of the histogram at 90 degrees in the red plot 92belonging to the 1:2 pulse sequence.

As will be appreciated by the person skilled in the art, if different RFmagnetic field pulses are used or gradients with different durations areused, the optimal ratio between the magnitude of first re-phasingmagnetic field gradient and the first magnetic field gradient to ensurethat the magnetisation are in-phase at the end of the MM pulse sequencemay differ.

FIG. 10 illustrates another exemplary MRI pulse sequence. This differsfrom the previous embodiment in that instead of applying a re-phasinggradient between the two slice selective rotations, the second gradientselected for the second slice selective rotation is arranged to performthe re-phasing role as described below.

This MM pulse sequence begins with a first radio-frequency magneticfield pulse (151) and a corresponding first magnetic field gradient 52that are used to excite nuclei within a part of a subject to perform afirst slice-selective rotation.

As noted above this first radio-frequency magnetic field pulse rotates anet magnetisation vector, about a first axis (e.g. the x axis) such thata portion of the magnetisation now lies in along the y axis. As with theprevious example the first slice selection gradient 52 is a magneticfield that has a magnitude that increases along direction that istransverse to the slice being imaged. For convenience this is deemed tobe a positive gradient.

Next a second radio-frequency magnetic field pulse (55A) andcorresponding second magnetic field gradient 54A is used to cause asecond slice-selective rotation. As with the previous embodiment thispulse and slice selection gradient cooperate to rotate the netmagnetisation about a second axis (the y axis in this example) such thatany residual magnetisation that existed along the z axis is rotated intothe x-y plane. Where this embodiment differs from the previousembodiment is that the second slice selection magnetic field gradient54A has a negative gradient compared to the first slice selectiongradient. That is, the magnetic field caused by the second sliceselection gradient decreases along the direction in which the firstslice selection gradient increases. This means that as well as enablingslice selection the gradient causes at least partial re-phasing of themagnetisation vectors that were de-phased (as illustrated in FIG. 6a )by the first slice selective rotation process.

As will be appreciated the first and second positive and negativegradients will need to be created so that the slices formed by eachgradient are in registration with each other. This may require thesecond RF pulse to have a negative frequency offset applied to so thatthe slice centres align along direction of the B0 field. This allowsslices offset from the centre of the magnet to be excited.

Finally, the pulse sequence includes final re-phasing magnetic fieldgradient to correct de-phasing of the magnetisation vectors within theensemble that are a result of the second slice-selective rotation. Finalre-phrasing magnetic field gradient in this case consists of a positivegradient of approximately half the duration of the gradient applied inthe previous slice selection gradient segment but equal size, as shownin FIG. 10.

FIGS. 9 to 20 illustrate a series of embodiments that include additionalslice selective rotations. In these examples three slice selectiverotations are used to achieve a desired rotation angle that isrelatively insensitive to B1 field inhomogeneity. In these examples themagnetisations are assumed to make clockwise rotations. It will beappreciated however that the methods disclosed herein can be applied,mutatis mutandis, to atoms whose magnetisations make anti clockwiserotations.

Turning firstly to FIG. 11, which illustrates a pulse sequence forachieving a rotation equivalent to a slice-selective 180 degreerefocussing pulse or an inversion pulse. In this example this isprovided by applying three successive 90 degree rotations and eachrotation is applied orthogonally to each previous rotation. In FIG. 11the top plot represents the RF magnetic field pulses B1, which in thisexample are shaped as sinc pulses. The lower plot illustrates appliedmagnetic field gradients.

For the refocussing pulse the magnetization is assumed to start in thex-y plane and must be “flipped-over” along an axis. This is illustratedschematically in FIGS. 12a to 12d by the rotational motion of the disk900. As can be seen the disk 900 is shown as initially lying in the x-yplane as it represents a multiplicity of magnetisations lying in thatplane but covering a range of phases. The disk is shown to have a topsurface 901 (shaded grey) and a bottom surface 902 (shaded white and notseen until FIG. 12d ). Datum points are also illustrated to assist invisualisation of the three dimensional motion of the disk 900. Thesedots include a single white dot initially (in FIG. 12a ) adjacent the +yaxis, a single black dot initially adjacent the −y axis. Both singledots are at a positive x-position. A pair of adjacent dots are alsoshown. The pair comprising a white dot in the +y side of the +x axis,and a black dot in the −y side of the +x axis.

The pulse sequence illustrated on FIG. 11 begins with a slice selectiverotation generated by the application of a first RF magnetic field pulse951 and an associated corresponding magnetic field gradient 952. Themagnetic field gradient has a magnitude that increases along a directiontransverse to a slice being selected. The slice selective rotation 951is configured to generate a 90 degree rotation (i.e. has a desiredrotation of 90 degrees) in the positive direction about the x axis. Therotation produces is shown in FIG. 12b . As can be seen the disk 900 hasrotated about the x axis as that it now lies in the x-z plane and no ymagnetisation.

Next a rephasing gradient 953 is applied with a reversed gradientdirection to the first slice selection magnetic field gradient 952. There-focussing magnetic field gradient 953 is generated to re-phase thede-phased gradients generated by the first slice selective rotation.

Then a second slice selective rotation is generated by the applicationof a second RF magnetic field pulse 954 and an associated correspondingsecond magnetic field gradient 955. The magnetic field gradient has amagnitude that increases along a direction transverse to a slice beingselected. The slice selective rotation 954 is configured to generate a90 degree rotation in the positive direction about the Y axis. Therotation is illustrated in FIG. 12c . As can be seen, as the diskrotates the pair of datum dots are now located adjacent the +z axis.

Next a rephasing gradient 956 is applied with a reversed gradientdirection to the second slice selection magnetic field gradient 955. There-focussing magnetic field gradient 956 is generated to re-phase thede-phased gradients generated by the first slice selective rotation.

Then a third slice selective rotation is generated by the application ofa third RF magnetic field pulse 957 and an associated correspondingthird magnetic field gradient 958. The magnetic field gradient has amagnitude that increases along a direction transverse to a slice beingselected. The third slice selective rotation 957 is also configured togenerate a 90 degree rotation in the positive direction about thex-axis. In this example the third slice selective rotation is generatedby application of an RF magnetic pulse and gradient field that areessentially the same as those used in the first slice selectiverotation. As shown in FIG. 12d this causes the disk 900 to flip over sothat side 902 is now on the side of the positive z axis and the pair ofdatum dots are now adjacent the positive y axis.

As can be seen the associated gradient waveform is symmetric, just likein the standard 180° refocusing pulse; the extra re-phasing gradientlobe not being required since the magnetization starts in the x-y planeand not along the z-axis. Note all three pulses are 90° and the signalexcited by the first pulse effectively experiences zero phase from thesubsequent four gradient lobes.

FIGS. 13a and 13b illustrate simulations of the Bloch equations for aconventional 180 degree refocussing pulse in (FIG. 13a ) and thatproduced by the 180 degree refocussing pulse sequence of FIG. 11. As canbe seen, in FIG. 13a the resultant magnetisation predominately lies inthe Mx direction. However the slice shape in the x and y directions issignificantly compromised away from the slice centre, and significantmagnetisation still exists at some values of z. In FIG. 13b simulationsfor the pulse sequence of FIG. 11 are shown. As can be seen the responsein the x and y directions are more rectangular (i.e. the slice has amore defined flat bottom and more “upright” clear cut-offs at theirsides. Much less signal remains in the z direction also.

As noted above this same pulse sequence can be used as a slice selective180 degree inversion pulse for a z-magnetisation. The rotation of thenet magnetisation in this case is illustrated in FIGS. 14a to 14d .Initially in FIG. 14a the net magnetisation M is aligned along thepositive z axis. The first slice selective rotation moves it into theposition shown in FIG. 14b in which M lies along the positive y axis.After re-phasing the magnetisation M is rotated about the y axis, whichdoes not cause any net movement of the magnetisations M. After the finalre-phasing the magnetisation is rotated again in the positivex-direction by 90° and, as shown in FIG. 14d ends up aligned along thenegative z axis.

FIG. 15 illustrates an alternative MRI pulse sequence equivalent to thatof FIG. 11, in that it is intended to produce the same effect as a 180degree re-focussing pulse, but which uses no dedicated re-focussinggradients. As disclosed in connection with the previous embodiment thepulse sequence includes first and third slice selective rotationscomprising respective RF magnetic field gradients 951, 957, andcorresponding slice selection gradients 952 and 958. However, in amanner analogous to FIG. 10, the pulse sequence of FIG. 15, inverts thedirection of the slice selection gradient 959 used for the second sliceselective rotation, so that it may also serve to perform refocussing.Furthermore the second RF magnetic field pulse 960 is applied with anegative phase when compared to the second RF pulse 954 of FIG. 11.Furthermore the second radio frequency magnetic pulse is also appliedwith a negative phase compared to the 2nd RF pulse in the firstembodiment. That is, the RF magnetic field B1b, in the case ofcircularly polarised RF magnetic fields, is −90° out of phase with thefirst RF magnetic field B1a.

Also as mentioned in relation to FIG. 10, the multiple slice selectivegradients will need to be performed so that their slices are inregistration with each other so appropriate frequency offsets will needto be applied to them so that they correctly align along the B0 field.

FIGS. 16a and 16b illustrate simulations of the Bloch equations for aconventional 180 degree inversion pulse in (FIG. 16a ) and that producedby the 180 degree inversion pulse sequence of FIG. 11(FIG. 16b ).

FIG. 17 illustrates a method of performing a rotation equivalent to a 90degree excitation pulse. In this example this is provided by applyingthree successive 45 degree rotations. In this example each rotation isapplied orthogonally to each previous rotation, and includes applicationof a final refocussing gradient after all slice selection gradients havebeen applied. As with previous examples, clockwise rotations of themagnetisations are assumed in the following description, and the initialnet magnetisation M lies along the positive z-axis.

As in the previous embodiments, the top plot shows the RF magnetic fieldpulses B1, which in this example are shaped as sinc pulses. The lowerplot illustrates applied magnetic field gradients G. A slice selectiverotation generated by the application of a first RF magnetic field pulse1251 and an associated corresponding magnetic field gradient 1252 areapplied. The magnetic field gradient has a magnitude that increasesalong a direction transverse to a slice being selected. The sliceselective rotation caused by first RF magnetic field pulse 1251 isconfigured to generate a 45 degree rotation (i.e. has a desired rotationof 45 degrees) in the positive direction about the x-axis.

Next a rephasing gradient 1253 is applied with a reversed gradientdirection to the first slice selection magnetic field gradient 1252. There-focussing magnetic field gradient 1253 is generated to re-phase thede-phased magnetisations generated by the first slice selectiverotation.

Then a second slice selective rotation is generated by the applicationof a second RF magnetic field pulse 1254 and an associated correspondingsecond magnetic field gradient 1255. The magnetic field gradient has amagnitude that increases along a direction transverse to a slice beingselected. The slice selective rotation 1254 is configured to generate a45 degree rotation in the positive direction about the y-axis.

Next a rephasing gradient 1256 is applied with a reversed gradientdirection to the second slice selection magnetic field gradient 1255.The re-focussing magnetic field gradient 1256 is generated to re-phaseand de-phased magnetisations generated by the first and second sliceselective rotation.

Then a third slice selective rotation is generated by the application ofa third RF magnetic field pulse 1257 and an associated correspondingthird magnetic field gradient 1258. The magnetic field gradient has amagnitude that increases along a direction transverse to a slice beingselected. The third slice selective rotation 1257 is also configured togenerate a 45 degree rotation in the positive direction about thex-axis. In this example, the third slice selective rotation is generatedby application of an RF magnetic pulse and gradient field that areessentially the same as those used the first slice selective rotation.The net result is that the magnetisation M will now lie in the x-yplane.

Lastly a final re-phasing magnetic field gradient 1259 is applied tocorrect de-phasing of the magnetisation vectors within the ensemble thatresulted from the previous slice-selective rotation.

FIG. 18 illustrates an alternative MRI pulse sequence equivalent to thatof FIG. 17, in that it is intended to produce the same effect as a 90degree excitation pulse, but which uses only a final re-focussinggradient and inverts the direction of the slice selection gradient usedfor the second slice selective rotation, so that it may also serve toperform some refocussing. As disclosed in connection with the previousembodiment the pulse sequence includes first and third slice selectiverotations comprising respective RF magnetic field gradients 1251, 1257,and corresponding slice selection gradients 1252 and 1258. It alsoincludes a final refocussing gradient 1259. However, in a manneranalogous to FIG. 10 (and FIG. 15), the pulse sequence of FIG. 18,inverts the direction of the slice selection gradient 1260 used for thesecond slice selective rotation, so that it may also serve to performrefocussing. Furthermore the second RF magnetic field pulse 1261 isapplied with a negative phase when compared to the second RF pulse 1254of FIG. 17. As previously noted, the multiple slice selective gradientsare performed so that their slices are in registration with each otherso appropriate frequency offsets will need to be applied to them so thatthey correctly align along the B0 field.

It is important to note that the present invention should not beconsidered as being limited to the production of certain specificdesired rotations, or using certain specific component rotations orcertain specific numbers of fixed rotations. In the examples describedherein each individual rotation is less than or equal to the totaldesired rotation, but the total cumulative rotation performed is greaterthan the total desired rotation.

FIGS. 19 and 20 illustrate simulations of the Bloch equations for aconventional 90 degree excitation pulse in (FIG. 19) and that producedby the 90 degree excitation pulse sequence of FIG. 17 (FIG. 20). Theconventional 90 degree excitation pulse is ideally intended to move allmagnetisation from the z direction and produce zero magnetisation in thex and z direction (i.e. Mx=Mz=0 across the whole slice), and allmagnetisation lies in the y direction.

In FIG. 20, simulations for the pulse sequence of FIG. 17 are shown. Thepulse aims to have zero magnetisation in the z direction (Mz) and allmagnetisation in the x and y plane. As can be seen the response in the xand y directions, produce a relatively flat response across the wholeslice. The Mz magnetisation clearly reaches the zero level across thecentral third of the slice.

Advantageously, the multiple pulse MRI sequences described herein areless sensitive to inhomogeneity in the first RF magnetic field affectingthe first rotation angle as the subsequent RF magnetic fields in the MRIsequence can be used to at least partially correct for a deviation ofthe first rotation angle from the intended angle due to the effect oftransverse magnetic field (B1) inhomogeneity. As a result, the effect ofthe spatial inhomogeneity of the B1 field on the MRI signal is reduced.This is to say that areas of a 2D image of a corresponding 2D slice, inthe x-y plane, of a subject that would otherwise be affected by thespatial inhomogeneity, are not affected as much (or not at all if theresultant first rotation angle was 45°, 90° or 135′). Furthermore, inpreferred forms the multiple pulse MM sequences described herein areapplied without requiring prior knowledge of which part of the image isaffected by inhomogeneity. Advantageously, imaging of areas that areaffected by inhomogeneity are improved without affecting the imageobtained from areas that are unaffected by inhomogeneity.

Whilst embodiments of the present invention can be used at any B0 fieldstrength, inhomogeneity in the B1 field may be more prevalent at higherB0 field levels, e.g. at 3 T or above. Hence some embodiments may beadvantageously used at B0 field levels of 3 T and above, such as 7 T.However, as discussed below, some embodiments of the present inventionalso provide improved signal strength (e.g. total received signalenergy). Thus whilst B1 inhomogeneity is less of a problem at a B0 levelof lower than 3 T, some embodiments may be present advantages. Henceembodiments can be used with B0 filed levels at 1.5 T, above 1.5 T orbelow 1.5 T.

FIG. 21 illustrates simulations of the total received signal strength,for a conventional 90 degree sinc pulse (Sinc 90) and the followingequivalent 90 degree pulse sequences:

-   -   A three component 90 degree pulse, such as that illustrated in        FIG. 17 (1-1-1 90);    -   A two component pulse having pulse components in a rotation        angle ratio of 1:2, such as that illustrated in FIG. 4 (1-2 90);    -   A two component pulse having pulse components in a rotation        angle ratio of 1:1(1-1 90).

Each point on each plot corresponds to the total received signal energyfrom within the selected imaging slice for a given level of input RFamplitude. As will be understood, it is desirable to have higherreceived signal level and also for the signal level to be relativelyconsistent across different RF amplitudes.

As can be seen, in each case the multiple-component pulse sequences ofembodiments of the present invention achieve a higher peak signalstrength than the conventional 90° sinc pulse. Moreover the curves arerelatively flatter than the conventional 90° sinc pulse.

FIG. 22 illustrates simulations of the total received signal strengthfrom within the selected imaging slice, for a conventional 180 degreesinc pulse (Sinc 180) and a three-component 180 degree inversion pulsesequence of the present invention, as illustrated in FIG. 11, plottedover a range of RF signal amplitudes, (1-1-1 180). As can be seen, themultiple-component pulse sequence of the inventive embodiment achieves ahigher peak signal strength than the conventional 180° sinc pulse.Moreover the curve is flatter than the conventional 180° sinc pulse.

FIG. 23 illustrates simulations of the total received signal strengthfrom within the selected imaging slice, for a conventional 180 degreesinc refocusing pulse (Sinc-refocus) and a three-component 180 degreerefocussing pulse sequence of the present invention, as illustrated inFIG. 11, plotted over a range of RF signal amplitudes, (1-1-1 refocus).As can be seen, the multiple-component pulse sequence of the inventiveembodiment achieves a higher peak signal strength than the conventional180° sinc refocusing pulse. Moreover the curve is flatter than theconventional 180° sinc refocussing pulse.

It will be understood that the invention disclosed and defined in thisspecification extends to all alternative combinations of two or more ofthe individual features mentioned or evident from the text or drawings.All of these different combinations constitute various alternativeaspects of the invention.

What is claimed is:
 1. A method for use in magnetic resonance imagingincluding: exposing at least a portion of a subject to a longitudinalmagnetic field (B0) such that a net magnetisation vector representing aresultant magnetisation of the nuclear magnetic moments of an ensembleof nuclei in the portion of the subject is longitudinally aligned withthe magnetic field (B0); performing a first slice-selective rotation byexposing at least said portion of the subject to a first radio-frequencymagnetic field pulse (B1a) and a corresponding first magnetic fieldgradient to excite nuclei within the portion of the subject, the firstradio-frequency magnetic field pulse being configured to rotate the netmagnetisation about a first axis by a first angle such that a firstcomponent of the net magnetisation lies in a first plane including thefirst axis and a second component of the net magnetisation remainsaligned with the magnetic field (B0); performing a secondslice-selective rotation by exposing at least said portion of thesubject to a second radio-frequency magnetic field pulse (B1b) andcorresponding second magnetic field gradient to excite nuclei within theportion of the subject, the second radio-frequency magnetic field pulsebeing configured to rotate the net magnetisation about a second axis bya second angle substantially equal to the first angle such that at leasta portion of the net magnetisation that remained aligned with themagnetic field (B0) after the first slice selective rotation lies in aplane including the second axis of rotation; and performing a thirdslice-selective rotation by exposing at least said portion of thesubject to a third radio-frequency magnetic field pulse (B1c) and acorresponding third magnetic field gradient to excite nuclei within theportion of the subject, the third radio-frequency magnetic field pulsebeing configured to rotate the net magnetisation about the first axis bya third angle substantially equal to the first and second angle.
 2. Themethod of claim 1, wherein both the first axis and second axis areorthogonal to the magnetic field (B0).
 3. The method of claim 2, whereinthe first axis and second axis are orthogonal to each other in arotating frame of reference about the longitudinal direction.
 4. Themethod of claim 1, further including performing a first phase adjustmentbefore the second slice selective rotation by exposing at least saidportion of the subject to a first re-phasing magnetic field gradient tocorrect de-phasing of magnetisation vectors within the ensemble that isa result of the first slice-selective rotation.
 5. The method of claim1, further including performing a second phase adjustment before thethird slice selective rotation by exposing at least said portion of thesubject to a second re-phasing magnetic field gradient to correctde-phasing of magnetisation vectors within the ensemble that is a resultof the second slice-selective rotation.
 6. The method of claim 1,wherein the second magnetic field gradient causes re-phasing of themagnetisation vectors that are de-phased by the first slice selectiverotation.
 7. The method of claim 1, wherein the second magnetic fieldgradient causes over-correcting said de-phasing of the magnetisationvectors within the ensemble.
 8. The method of claim 7, wherein theovercorrection is such that the third slice selective rotation causedre-phasing of the magnetisation vectors within the ensemble.
 9. Themethod of claim 1, further including performing a final phase adjustmentafter the third slice selective rotation by exposing at least saidportion of the subject to a final re-phasing magnetic field gradient tocorrect de-phasing of magnetisation vectors within the ensemble.
 10. Themethod of claim 1, wherein the magnetic field (B0) has a magnitude of atleast 1.5 T.
 11. A magnetic resonance imaging (MRI) system including:magnetic field producing means for producing a magnetic field (B0);magnetic field gradient producing means configured to produce magneticfield gradients to alter the magnetic field B0 and produce an effectivemagnetic field; radio-frequency magnetic field generating meansconfigured to produce radio-frequency magnetic fields (B1a and B1b); andpositioning means for positioning at least part of a subject to beexposed to the effective magnetic field; the system being configured toperform a method as claimed in claim
 1. 12. A method for use in magneticresonance imaging including: exposing at least a portion of a subject toa longitudinal magnetic field (B0) such that a net magnetisation vectorrepresenting a resultant magnetisation of the nuclear magnetic momentsof an ensemble of nuclei in the portion of the subject is longitudinallyaligned with the magnetic field (B0); performing a first slice-selectiverotation by exposing at least said portion of the subject to a firstradio-frequency magnetic field pulse (B1a) and a corresponding firstmagnetic field gradient to excite nuclei within the portion of thesubject, the first radio-frequency magnetic field pulse being configuredto rotate the net magnetisation about a first axis by a first angle suchthat a first component of the net magnetisation lies in a first planeincluding the first axis and a second component of the net magnetisationremains aligned with the magnetic field (B0); performing a secondslice-selective rotation by exposing at least said portion of thesubject to a second radio-frequency magnetic field pulse (B1b) andcorresponding second magnetic field gradient to excite nuclei within theportion of the subject, the second radio-frequency magnetic field pulsebeing configured to rotate the net magnetisation about a second axis bya second angle of substantially twice the magnitude of the first anglesuch that at least a portion of the net magnetisation that remainedaligned with the magnetic field (B0) after the first slice selectiverotation lies in a plane including the second axis of rotation; andperforming a final phase adjustment by exposing at least said portion ofthe subject to a final re-phasing magnetic field gradient to correctde-phasing of the magnetisation vectors within the ensemble that existafter the second slice-selective rotation.
 13. The method of claim 12,wherein at least one of the first and second axis is orthogonal to themagnetic field (B0).
 14. The method of claim 12, wherein the first axisand the second axis lie in a transverse plane orthogonal to the magneticfield (B0).
 15. The method of claim 12, wherein the first axis and thesecond axis are orthogonal to each other in a rotating frame ofreference about the longitudinal direction.
 16. The method of claim 12,further including performing a first phase adjustment before the secondslice selective rotation by exposing at least said portion of thesubject to a first re-phasing magnetic field gradient to correctde-phasing of magnetisation vectors within the ensemble that is a resultof the first slice-selective rotation.
 17. The method of claim 16,wherein any one or more of the following relationships hold between thefirst magnetic field gradient and the first re-phasing magnetic fieldgradient: an integral of the amplitude of first magnetic field gradientover time is equal to an integral of amplitude of the first re-phasingmagnetic field gradient over time; the duration of the first magneticfield gradient is longer than the duration of the first re-phasingmagnetic field gradient; and the magnitude of the first re-phasingmagnetic field gradient is at least twice the magnitude of the firstmagnetic field gradient.
 18. The method of claim 16, wherein the firstphase adjustment further includes over-correcting said de-phasing of themagnetisation vectors within the ensemble.
 19. The method of claim 18,wherein the second magnetic field gradient causes re-phasing of theover-corrected magnetisation vectors such that a temporal centre of thesecond radio-frequency pulse substantially coincides with a time atwhich the magnetisation vectors within the ensemble are substantially inphase.
 20. The method of claim 12, wherein following the final phaseadjustment the magnetisation vectors within the ensemble aresubstantially in phase.
 21. The method of claim 12, wherein the magneticfield (B0) has a magnitude of at least 1.5 T.
 22. A magnetic resonanceimaging (MRI) system including: magnetic field producing means forproducing a magnetic field (B0); magnetic field gradient producing meansconfigured to produce magnetic field gradients to alter the magneticfield B0 and produce an effective magnetic field; radio-frequencymagnetic field generating means configured to produce radio-frequencymagnetic fields (B1a and B1b); and positioning means for positioning atleast part of a subject to be exposed to the effective magnetic field;the system being configured to perform a method as claimed in claim 12.23. A method for use in magnetic resonance imaging including: exposingat least a portion of the subject to a longitudinal magnetic field (B0)such that a net magnetisation vector representing a resultantmagnetisation of the nuclear magnetic moments of an ensemble of nucleiin the portion of the subject is longitudinally aligned with themagnetic field (B0); performing a first slice-selective rotation byexposing at least said portion of the subject to a first radio-frequencymagnetic field pulse (B1a) and a corresponding first magnetic fieldgradient to excite nuclei within the portion of the subject, the firstradio-frequency magnetic field pulse being configured to rotate the netmagnetisation about a first axis by a first angle such that a firstcomponent of the net magnetisation lies in a first plane including thefirst axis and a second component of the net magnetisation remainsaligned with the magnetic field (B0); performing a first phaseadjustment by exposing at least said portion of the subject to a firstre-phasing magnetic field gradient to correct de-phasing ofmagnetisation vectors within the ensemble that is a result of the firstslice-selective rotation, and to over-correct said de-phasing of themagnetisation vectors within the ensemble; performing a secondslice-selective rotation by exposing at least said portion of thesubject to a second radio-frequency magnetic field pulse (B1b) andcorresponding second magnetic field gradient to excite nuclei within theportion of the subject, the second radio-frequency magnetic field pulsebeing configured to rotate the net magnetisation about a second axis bya second angle of substantially twice the magnitude of the first angle,such that at least a portion of the net magnetisation that remainedaligned with the magnetic field (B0) after the first slice selectiverotation lies in a plane including the second axis of rotation; andperforming a final phase adjustment by exposing at least said portion ofthe subject to a final re-phasing magnetic field gradient to correctde-phasing of the magnetisation vectors within the ensemble that is aresult of the second slice-selective rotation.
 24. A method of claim 23,wherein the second magnetic field gradient causes re-phasing of theover-corrected magnetisation vectors such that a temporal centre of thesecond radio-frequency magnetic field pulse substantially coincides witha time at which the magnetisation vectors within the ensemble aresubstantially in phase.
 25. The method of claim 23, wherein followingthe final phase adjustment the magnetisation vectors within the ensembleare substantially in phase.
 26. The method of claim 23, wherein at leastone of the first axis and second axis is orthogonal to the magneticfield (B0).
 27. The method of claim 23, wherein the first axis and thesecond axis lie in a transverse plane orthogonal to the magnetic field(B0).
 28. The method of claim 23, wherein the first axis and second axisare orthogonal to each other in a rotating frame of reference about thelongitudinal direction.
 29. The method of claim 23, wherein any one ormore of the following relationships hold between the first magneticfield gradient and the first re-phasing magnetic field gradient: anintegral of the amplitude of first magnetic field gradient over time isequal to an integral of amplitude of the first re-phasing magnetic fieldgradient over time; the duration of the first magnetic field gradient islonger than the duration of the first re-phasing magnetic fieldgradient; and the magnitude of the first re-phasing magnetic fieldgradient is at least twice the magnitude of the first magnetic fieldgradient.
 30. A magnetic resonance imaging (MRI) system including:magnetic field producing means for producing a magnetic field (B0);magnetic field gradient producing means configured to produce magneticfield gradients to alter the magnetic field B0 and produce an effectivemagnetic field; radio-frequency magnetic field generating meansconfigured to produce radio-frequency magnetic fields (B1a and B1b); andpositioning means for positioning at least part of a subject to beexposed to the effective magnetic field; the system being configured toperform a method as claimed in claim 23.